Every now and then, there has been natural or man-made calamities. Such adversities instigate various institutions to find solutions for them. The current study attempts to explore the disaster caused by the micro enemy called coronavirus for the past few months and aims at finding the solution for the system of nonlinear ordinary differential equations to which q−homotopy analysis transform method (q−HATM) has been applied to arrive at effective results. In this paper, there are eight nonlinear ordinary differential equations considered and to solve them the advanced fractional operator Atangana-Baleanu (AB) fractional derivative has been applied to produce better understanding. The outcomes have been presented in terms of plots. Ultimately, the present study assists in examining the real-world models and aids in predicting their behavior corresponding to the parameters considered in the models. KEYWORDS Atangana-Baleanu fractional derivative, coronavirus epidemic model, nonlinear differential equations, q−homotopy analysis transform method MSC CLASSIFICATION 37M05; 34F05; 92D30 1 INTRODUCTION Human history is facing a strange time, fighting with an invisible enemy called the novel coronavirus (COVID-19). This pandemic virus disease found in Wuhan, China. 1 It ensured where the animals and sea meat were sold and named as coronavirus on 31st of December, 2019. The Chinese Government and its health organization together insisted about its transformation from animals to human. 2,3 Coronavirus spread is rapidly increasing in all over the countries. Large number of people are affected by this deadly disease. The current status of coronavirus (COVID-19) is unimaginable, because enormous people have been suffered so far. Though people are recovering from this COVID-19, simultaneously the death ratio is increasing rapidly. World health organization is giving awareness among people through various factors. Scientist are also insisting its importance. The entire nation is joining together to overcome the disease, because even the developed countries couldn't get solution for this virus. This disease threat the people all over the world mentally, because vaccine didn't find yet for this dreadful disease. This study is not only on anticipating the results of the spread but also analyzing the spread of various disease. The study also focuses on to control the disease as possible. 1,4-8 In this paper, we are applying q-homotopy analysis transformation method (q-HATM) to the system of nonlinear equations and find suitable solution for this crucial disease. In order to consider the new fractional operator called

The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, chemistry, biology, and mathematics. One of the most important characteristics in the expressive assessment and development of computational design techniques is symmetry. Yet, mathematical models are an important method of studying real-world systems. The symmetry reflected by such a mathematical model reveals the inherent symmetry of real-world systems. This study focuses on the contagious model of pine wilt disease and symmetry, employing the q-HATM (q-Homotopy Analysis Transform Method) to the leading fractional operator Atangana–Baleanu (AB) to arrive at better understanding. The outgrowths are exhibited in the forms of figures and tables. Finally, the paper helps to analyze the practical theory, assisting the prediction of its manner that corresponds to the guidelines when contemplating the replica.

Human survival is purely based on the environment. Through natural calamities or man-made depredation, the pleasant existence is disturbed. Trees provide not just foliage for the environment but also a pleasant atmosphere for the human population. One of the most serious threats to the forest and ecology is the pine wilt disease (PWD). It is a devastating disease that kills pine trees in a matter of weeks. The pine-wood nematode Bursaphelenchus Xylophilus causes PWD. This study emphasises on the infectious model of PWD engaging the [Formula: see text]-homotopy analysis transform method ([Formula: see text]-HATM) to a leading fractional operator Caputo–Fabrizio fractional time derivative to arrive for superior understanding. The denouements are presented in the forms of plots and tables. At last the paper supports to examine the real-world models and helps to forecast their behavior that communicate the instructions considered in the models.